Broad band sparse spectra are very common; such spectra are generated whenever a modulated sinusoidal carrier passes through a dead zone, a limiter, a rectifier, or any other single valued nonlinearity, whether desired or not, or even in the case where the carrier is not a perfect sinusoid. Some of these nonlinearities can occur to some extent in anti-aliasing or low-pass filters (LPF), and use of this method of sampling can therefore offer many disadvantages to digital systems. For example, anti-aliasing filters consume power, require space, evolve undesirable heat, contribute error to the digital system which follows the sampler and quantitizer, are costly, and are a potential source of failures.
Known digital sampling techniques require that each channel which is to be sampled be preconditioned as, for example, with low-pass filters. In the context of capacitive fuel quantity, this preconditioning may require one LPF for each probe, or each group of probes connected in parallel, with the result that the aforementioned undesirable factors--cost, weight, power, heat, space, phase and gain changes and other errors--are introduced into the digital system. It is therefore advantageous not only to omit the use of anti-aliasing pre-filters in digital sampling techniques, but to sample as well at the lowest possible frequencies, or equivalently to determine at the same time the largest sampling interval which has the desired non-aliasing property.